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Journal of Lie Theory 32 (2022), No. 2, 553--561
Copyright Heldermann Verlag 2022

Generic 1-Connectivity of Flag Domains in Hermitian Symmetric Spaces

Tatsuki Hayama
School of Business Administration, Senshu University, Kawasaki, Kanagawa, Japan

A flag domain is an open real group orbit in a complex flag manifold. It has been shown that a flag domain is either pseudoconvex or pseudoconcave. Moreover, generically 1-connected flag domains are pseudoconcave. In this study, for flag domains contained in irreducible Hermitian symmetric spaces of type AIII or CI, we determine which pseudoconcave flag domain is generically 1-connected.

Keywords: Flag domain, Hermitian symmetric space, Weyl group.

MSC: 14M15, 32M05, 57S20.

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